Optimal location and size of photovoltaic systems in high voltage transmission power networks

Electrical Engineering

Optimal location and size of photovoltaic systems in high voltage

transmission power networks

Bach Hoang Dinh a

, Thuan Thanh Nguyen b

, Thang Trung Nguyen a

, Thai Dinh Pham c,⇑

a Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Viet Nam b Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 700000, Viet Nam

c Institute of Research and Development, Duy Tan University, Danang 550000, Viet Nam

article info

Article history:

Received 18 May 2020

Revised 24 August 2020

Accepted 18 December 2020

Available online 31 March 2021

Keywords:

Optimal power flow

Fitness function

Fuel cost function

Photovoltaic system

Water Cycle Algorithm

abstract

This paper presents Water Cycle Algorithm (WCA) to solve the Optimal Power Flow (OPF) problem with

and without renewable energy sources. WCA has been tested on IEEE 30, 57, and 118-bus transmission

networks to find minimum fuel cost. Main parameters of WCA have been set to different values for sur￾veying the real performance and the best settings of the parameters have led to better results than those

of previous methods. In addition, the best appropriate parameters have also supported WCA in finding

the best location of a Photovoltaic system (PVS) in the first network. WCA could reach less power loss

than two other metaheuristics, especially reaching much less power loss than the case without PVS.

Consequently, WCA with the most appropriate parameter settings is really a powerful search method

in terms of quick convergence speed and high-quality global optimum for the OPF problem with large￾scale power networks.

2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni￾versity. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/

by-nc-nd/4.0/).

1. Introduction

Optimal Power Flow (OPF) is a vital function of the power sys￾tem analyses for planning and studying operation. The OPF

approaches have been developed by combining the optimization

and load flow algorithm so that setting control parameters of

power systems, i.e. power generators, node voltages, compensation

volumes, etc. are determined by optimizing single or multi objec￾tives but always satisfying main constraints [1]. In modern power

systems, especially in electricity markets, OPF is a complicated

problem due to the large scale non-convex and non-linear opti￾mization characteristics as well as the multi-task control aims,

which are operating cost, power losses, overload of transmission

lines, load voltage deviation, system voltage instability, etc. [2,3].

Therefore, the OPF is a fundamental tool for all processes of plan￾ning, operation and control of network dispatch centers and utili￾ties. Moreover, with the advances in computing capability and

new optimization algorithms, OPF could contribute to various

applications in power system operations, especially in transmis￾sion systems where the network reconstruction solutions are

involved various constraints and many different conditions inves￾tigated in scheduled period [4].

So far several analytical and conventionally advanced program￾ing methods have been used to solve the OPF problem, such as

gradient based method [1], quadratic programming (QP) [5],

Newton-based method [6,7], linear programming (LP) [8,9], non￾linear programming (NLP) [9] and interior point (IP) methods

[10]. However, as analyzed in [1,6,11], these traditional techniques

could not solve the complex objective functions which are not dif￾ferentiable as well as the presence of complicated constraints. The

convergence property of the NLP based OPF is insufficient due to

possibly occurring local minimums. On the other hand, the LP

based methods is unable to deal with the optimization problems

whose cost function is non-smooth. The QP based approaches

can be used just for the approximation case of the exact cost func￾tion by its piece-wise quadratic equivalents. And more importance,

all of these mentioned approaches are unable to solve the multi￾optimization problems. Therefore, the conventional solutions

https://doi.org/10.1016/j.asej.2020.12.015

2090-4479/
2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding author.

E-mail addresses: [email protected] (B.H. Dinh), nguyenthanhthuan@

iuh.edu.vn (T.T. Nguyen), [email protected] (T.T. Nguyen), phamdinhthai@

duytan.edu.vn (T.D. Pham).

Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

Ain Shams Engineering Journal 12 (2021) 2839–2858

Contents lists available at ScienceDirect

Ain Shams Engineering Journal

journal homepage: www.sciencedirect.com

based on the mathematical programming techniques may not

guarantee to converge to the global optimal point of general OPF

problems with non-convex objective functions, complicated con￾straint conditions and unable to solve multi-optimal purposes.

Instead of using conventional methods, alternative meta￾heuristic algorithms can be a promising and reliable trend to solve

the comprehensive OPF problems.

The meta-heuristic algorithms [11] differ from the conventional

optimization approaches in principle. The conventional optimiza￾tion algorithms use a single solution updated at every iteration

and also mainly use the mathematical techniques, e.g. gradient

descent method, for approaching the optimum solution. Its optimal

calculation starts from a random guess solution and then tries to

move to a better solution based on some pre-specified transition

rule where its search direction is derived from considering the

local information. Whereas, the meta-heuristics optimization

approaches implement the non-deterministic optimal search that

bases on the iterative improvement of candidate solutions to solve

complicated problems, which are very difficult or unable to solve

by conventional methods [11,12]. They can be seen as the search￾ing group in which many candidate solutions (tens to hundreds)

can be simultaneously created and compared over several itera￾tions. The search is continued for a number of times and the better

updated solutions, which are created from randomly heuristic

ways will replace to the older and poorer ones to rank the best

solutions. A multi-directional search is performed to find a best

solution not only on a local area but also the global space. How￾ever, their computational burden is too high and calculation time

must be longer than that of conventional approaches. Various

examples of meta-heuristic algorithms used for solving the OPF

problems can be listed in [13–42]. They can be applied to solve

the OPF with single or multi objectives. For single objective, the

OPF just determines the minimum cost and one of most popular

algorithms is based on Particle Swarm Optimization (PSO) [13]

and its modified versions, such as Evolving Ant Direction Particle

Swarm Optimization (EADPSO) [14], Improved Particle Swarm

Optimization (IPSO) [15], Graphics Processing Units Particle

Swarm Optimization (GPU-PSO) [16], Particle Swarm Optimization

and Pattern Search (PSO-PS) [17], and Hybrid Canonical Differen￾tial Evolutionary Particle Swarm Optimization (HC-DEEPSO) [18].

Another trend is based on Differential Evolution (DE) [19] and

the modified versions, such as Constraint Handling Techniques

with Differential Evolution (CHT-DE), Superiority of Feasibly

solutions with Differential Evolution (SP-DE) [20], and Efficient

Evolutionary Algorithm (EEA) [21]. The list can be added by

Biogeography-Based Optimization (BBO) [22], Adaptive Real Coded

Biogeography-Based Optimization (ARCBBO) [23], Improved Krill

Herd Algorithm (IKHA) [24], Developed Grey Wolf Optimizer

(DGWO) [25], Cuckoo Optimization Algorithm (COA) [26],

Improved Colliding Bodies Optimization (ICBO) [27], Moth Swarm

Algorithm (MSA) [28], Water Cycle Algorithm (WCA) [29],

Improved Bat Algorithm (IBA) [30], Tree-Seed Algorithm (TSA)

[31], Modified Sine-Cosine Algorithm (MSCA) [32], and High Per￾formance Social Spider Optimization (HP-SSO) [33]. Moreover,

meta-heuristic approaches for the multi-objective OPF problems

can be mentioned here such as Self-adaptive Penalty with Differen￾tial Evolution (SAP-DE) [20], EEA [21], Dragonfly Algorithm and

Particle Swarm Optimization (DA-PSO) [34], Modified Teaching–

Learning Based Optimization (MTLBO) [35], Multi-Objective Modi￾fied Imperialist Competitive Algorithm (MOMICA) [36], Decoupled

Quadratic Load Flow with Enhanced Genetic Algorithm (EGA–

DQLF) [37], Mixed Integer Non-Linear Programming (MINLP)

[38], Artificial Bee Colony (ABC) [39], Enhanced Ant Colony

Optimization (EACO) [40], and Moth-Flame Optimizer (MFO)

[41]. Furthermore, for the modern power systems integrated to

renewable sources, OPF based meta-heuristic algorithms can

determine not only the optimally operational variables but also

the best location for installing renewable sources. In [42], a Modi￾fied Coyote Optimization Algorithm (MCOA) has been proposed to

solve the OPF problem for the IEEE 30-bus system with the place￾ment of a Photovoltaic Source (PVS).

In this paper, a new approach based on Water Cycle Algorithm

(WCA) has been proposed to solve the OPF problem. This method

inspires from the natural water cycles where fundamental concepts

and ideas are based on the observation of water cycle process and

the way of rivers and streams flowing to the sea [12]. It has been suc￾cessfully applied to various constrained optimization problems in

electrical engineering field. In this research, the effectiveness of

the Water Cycle Algorithm (WCA) has been evaluated by the perfor￾mance in four test systems where their optimal power flow solutions

are discovered according to a single objective function of minimiz￾ing fuel cost. The simulation results have been compared to those

of various similar algorithms and they have proved the capability

of the proposed approach in solving the OPF problem.

In summary, the novelties of the paper are as follows:

1) Present the implementation of WCA for OPF problem where

PV systems are placed for minimizing total fuel cost of ther￾mal units,

2) Observe the impact of control parameters on the real perfor￾mance of WCA for OPF problem with and without the pres￾ence of PV systems.

Nomenclature

Qsci Reactive power generation of the ith capacitor bank

TCi Tap value of the transformer i

NTc Number of transformers in transmission network

VLi The ith load bus voltage magnitude

NLb Number of load buses in transmission network

Nl Number of transmission lines

SLm Apparent power flow in the mth transmission line

b Acceleration factor

Ds The random matric number between zero and one

e, e1 The random number between zero and one

FFk Fitness value of the kth considered solution

FFsea Fitness value of the sea

FFr

river Fitness function of the r

th river

FFs

stream Fitness function of the s

th stream

iter The current iteration

Miter The maximum iteration

Np Population size

Nsr The sum of rivers and the sea

Nr Number of rivers

Nstr Number of streams

NS Number streams flowing into the sea or rivers

Tolpre Maximum distance between two solutions

Wsea Position of the sea

Wr

river Position of the r

th river

Ws

stream Position of the s

th stream

Npv The number of PV systems installed in the considered

system

Bach Hoang Dinh, Thuan Thanh Nguyen, Thang Trung Nguyen et al. Ain Shams Engineering Journal 12 (2021) 2839–2858

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